How do you find the solution of the system of equations 3x-2y=10 and 5x+3y=15?

May 15, 2015

One easy way of solving this is by substitution. To do that, all you have to do is isolate one variable in one equation and substitute it in the other equation.

You can choose to isolate $x$ or $y$ in the first or the second equation. It doesn't matter. BUT after that you have to substitute the value you find in the OTHER equation, alright?

So, let's do it by isolating $y$ in the first equation.

$3 x - 2 y = 10$
$- 2 y = 10 - 3 x$
$y = - 5 + \frac{3 x}{2}$

Now you just have to substitute this value of $y$ in the second equation.

$5 x + 3 \left(- 5 + \frac{3 x}{2}\right) = 15$
$5 x - 15 + \frac{9 x}{2} = 15$
$\frac{1 x}{2} = 30$
$x = 30 \cdot 2 = 60$
$x = 60$

If $x = 60$ and the value of $y$ is given by $y = - 5 + \frac{3 x}{2}$, then:

$y = - 5 + \frac{3 \left(60\right)}{2} = - 5 + \frac{180}{2} = - 5 + 90 = 85$